Question

The Buyer's Guide of the Web site for Car and Driver magazine provides reviews and road tests for cars, trucks, SUVs, and Vans. The average ratings of overall quality, vehicle styling, braking, handling, fuel economy, interior comfort, acceleration, dependability, fit and finish, transmission, and ride are summarized for each vehicle using a scale ranging from 1 (worst) to 10 (best). A portion of the data for a number of Sports/GT cars is shown as follows: Overall qualityHandlingFit and Finish Dependability Sports/GT 7.67 8.97 9.38 8.55 7.87 7.34 7.93 8.07 8.12 8.33 7.36 8.21 9.55 7.97 Acura 3.2CL Acura RSX Audi TT BMW 3 series/M3 Chevrolet Corvette Ford Mustang Honda Civic Si Infiniti G35 Mazda RX-8 Mini Cooper Mitsubishi Eclipse Nissan 350Z Porsche 911 Toyota Celica 7.80 9.02 9.00 8.39 8.82 8.34 8.92 8.70 8.58 8.76 8.17 8.07 9.55 8.77 7.83 9.46 9.58 9.52 9.64 8.85 9.31 9.34 9.79 10.00 8.95 9.35 9.91 9.29 8.17 9.35 8.74 8.39 8.54 8.70 9.50 8.96 8.96 8.69 8.25 7.56 8.86 9.04 A). Write down the equation of the sample regression line and carefully interpret the meaning of the coefficients. B) At 5% level of significance, is there sufficient evidence of a linear relationship between handling and the overall quality? You must show all necessary work for your analysis to be statistically val C) At 5% level of significance, is there sufficient evidence of a linear relationship between fit and finish and the overall quality? You must show all necessary work for your analysis to be statistically vali D) At 5% level of significance, is there sufficient evidence of a linear relationship between dependability and the overall quality? You must show all necessary work for your analysis to be statistically vali E). At 5% level of significance, is there sufficient evidence to conclude that the linear model is useful? You must show all necessarv work for vour analvsis to be statisticallv valid. F). Assess the linear model and explain carefully the procedures used in the assessment. G). Carefully explain the concept of collinearity. Is there evidence of noticeable collinearity as far as the statistical analysis you have performed in this problem? Explain carefully. What is your opinion and recommendation about handling as a variable in the linear model and whether or not it contributes information for the prediction of the overall quality? Explain very carefully. H). Examine the residual plots. Carefully explain what information each plot provides in terms of the above study?

Answer 1

We will use MINITAB software to get the answers,

a)

The regression equation is
overall quality = 2.11 + 0.407 heading + 0.262 fit and finish
+ 0.0662 dependability

here we get all coefficient has positive value,

interpretation :

heading: keeping all variable as constant if we increase one unit of heading then we get 0.407 times increase in overall quality.

fit and finish: keeping all variable as constant if we increase one unit of fit and finish then we get 0.262 times increase in overall quality.

dependability: keeping all variable as constant if we increase one unit of dependability then we get 0.0662 times increase in overall quality.

The MINITAB output for significance of all variable is

Predictor Constant heading fit and finish 0.2625 0.1557 1.69 0.123 dependability 0.06624 0.08777 0.75 0.468 Coef SE Coef T 2.108 1.576 1.34 0.211 0.4070 0.1876 2.17 0.055 S: 0.298311 R-Sq 66.5% R-Sq ( adj ) :56.4% -

b)

given significance level=0.05

here p-value for heading = 0.055>0.05 hence we can say that heading is insignificant to predict overall quality.

c)

here p-value for fit and finish= 0.123>0.05 hence we can say that fit and finish is insignificant to predict overall quality.

d)

here p-value for dependability= 0.468>0.05 hence we can say that dependability is insignificant to predict overall quality.

e)

there is no variable can significantly predict overall quality.

but taking all variables and by ANOVA table we get

Analysis of Variance DF MS F Source Regression Residual Error 10 0.88989 0.08899 Total 3 1.76506 0.58835 6.61 0.010 13 2.65495

so here p-value = 0.01 < 0.05 hence we can say that the model is significantly effective.

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